Question

Solve for x.

Answer 1

Now I think I know how to sort of do it. What I got is that I put it into 8x/5x+3=10x-2/7x and then I cross multiply and i get 56x^2 = 5x+3(10x-2) and now I think I use the FOIL method to distribut 5x+3 into 10x-2 and I then get 56x^2=10x^2+40x6...so do I have it good so far? What do i do next?

Answer 2

What do you mean? Arent I supposed to use the Triangle- Angle - Bisector Theorem?

Answer 3

Your solution is only true if the two triangles are proven to be similar.

Answer 4

no, @jewlzme17 is right, that theorem works.

Answer 5

thank you, okay so then did I do something wrong? and what am I supposed to do next?

Answer 6

it's a quadratic equation! you know what it is @jewlzme17

Answer 7

yes

Answer 8

(5x+3)(10x-2) = 50x^2 +20x - 6
50x^2 +20x - 6 = 56x^12

Answer 9

\[\frac{ 10x-2 }{ 7x }=\frac{ 8x }{ 5x+3 }\]
so
\[(10x-2)(5x+3)=(7x)(8x)\]
\[50x ^{2}+20x-6=56x ^{2}\]
\[-6x ^{2}+20x-6=0\]factor that to get
\[(-3x+1)(2x-6)=0\]

Answer 10

Then,
6x^2 - 20x +6 = 0
3x^2 - 10x + 3 = 0
(3x-1) (x-3) = 0
Hence x = 1/3 and 1

Answer 11

1/3 and 3, according to my explanation

Answer 12

okay so then that would be x?

Answer 13

2 answers, x=1/3 for sure and I got x=3 for the other, though @Yttrium got x=1

Answer 14

oh sorry. it's 3.

Answer 15

Both of our explanations are right, tho different methods.

Answer 16

it just implies that there are two possible solutions for x. it can be 1/3 or 3.

Answer 17

oh okay! Thank you guys :)